CSAT 2024

Q. A person buys three articles p, q and r for 50. The price of the article q is 16 which is the least.

Question: What is the price of the article p?

Statement-I: The cost of p is not more than that of r.

Statement-II: The cost of r is not more than that of p.

Which one of the following is correct in respect of the above Question and the Statements?
a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
b) The Question can be answered by using either Statement alone
c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone
d) The Question cannot be answered even by using both the Statements together
Correct answer: c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone

Question from UPSC Prelims 2024 CSAT

Explanation : 

Total Cost:
p + q + r = 50
Given q = 16 (the least),
p + r = 34

Statement I: p ≤ r

Possible pairs (p, r):
p = 16, r = 18
p = 17, r = 17
Conclusion: p can be 16 or 17. Statement I alone insufficient.

Statement II: r ≤ p

Possible pairs (p, r):
p = 17, r = 17
p = 18, r = 16
Conclusion: p can be 17 or 18. Statement II alone insufficient.

Using Both Statements Together:
p ≤ r and r ≤ p imply p = r
Thus, p = r = 17
Conclusion: p is uniquely determined as 17 using both statements.

Answer: c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone.

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